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Central Configurations of the Five-Body Problem with Equal Masses

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Tsung-Lin Lee, Manuele Santoprete

Mathematical Physics · Submitted 31 May 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses.

how it is stated · asserted 1.00 read the record →

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arXiv ID0906.0148 (version 1)
Pith IDGP77N4R5, Pith's permanent record of this paper and its review
CitationManuele Santoprete, Tsung-Lin Lee. "Central Configurations of the Five-Body Problem with Equal Masses." arXiv:0906.0148 (2009). https://pith.science/paper/GP77N4R5
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,558 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.16 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. contribution 0.93 0.95 0.89 asserted 1.00
s1 This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. method 1.00 0.90 0.04 asserted 1.00
s2 The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. method 1.00 0.88 0.04 asserted 1.00
s3 Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time. interpretation 0.58 0.71 0.08 hedged possibility 0.79

What kind of paper the classifier reports this is: theoretical result 0.89 · evidence from simulation or computation 0.99.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we present a complete classification of the isolated central configurations of the five-body problem with equal masses. This is accomplished by using the polyhedral homotopy method to approximate all the isolated solutions of the Albouy-Chenciner equations. The existence of exact solutions, in a neighborhood of the approximated ones, is then verified using the Krawczyk method. Although the Albouy-Chenciner equations for the five-body problem are huge, it is possible to solve them in a reasonable amount of time.

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